Question

The figure below is a scale drawing of an office courtyard using the scale 1 centimeter = 4 feet.

Image shows a quadrilateral with sides 75 cm, 30 cm, 72 cm and 51 cm

Which figure is a scale drawing of the same courtyard using the scale 1 centimeter = 3 feet?

A.
Image shows a quadrilateral with sides 100 cm, 40 cm, 86 cm and 58 cm
B.
Image shows a quadrilateral with sides 25 cm, 10 cm, 24 cm and 17 cm
C.
Image shows a quadrilateral with sides 100 cm, 40 cm, 96 cm and 68 cm
D.
Image shows a quadrilateral with sides 25 cm, 10 cm, 22 cm and 19 cm

Answer 1

To solve this problem, we need to first convert the original dimensions of the courtyard from the scale of 1 centimeter = 4 feet to their actual dimensions, and then convert those dimensions to a new scale of 1 centimeter = 3 feet.

**Step 1: Convert Scale Drawings to Actual Dimensions**

For the given quadrilateral with sides 75 cm, 30 cm, 72 cm, and 51 cm using the scale of 1 cm = 4 feet:

- 75 cm = 75 * 4 = 300 feet
- 30 cm = 30 * 4 = 120 feet
- 72 cm = 72 * 4 = 288 feet
- 51 cm = 51 * 4 = 204 feet

So, the actual dimensions of the courtyard are 300 feet, 120 feet, 288 feet, and 204 feet.

**Step 2: Convert Actual Dimensions to New Scale**

Now, we will convert these dimensions to a scale of 1 cm = 3 feet:

- For 300 feet: 300 feet / 3 feet/cm = 100 cm
- For 120 feet: 120 feet / 3 feet/cm = 40 cm
- For 288 feet: 288 feet / 3 feet/cm = 96 cm
- For 204 feet: 204 feet / 3 feet/cm = 68 cm

**Step 3: Compare with the Given Options**

Now, we need to check which of the options matches the dimensions we calculated (100 cm, 40 cm, 96 cm, 68 cm):

A. 100 cm, 40 cm, 86 cm, 58 cm
B. 25 cm, 10 cm, 24 cm, 17 cm
C. 100 cm, 40 cm, 96 cm, 68 cm
D. 25 cm, 10 cm, 22 cm, 19 cm

The only option that matches the calculated dimensions (100 cm, 40 cm, 96 cm, and 68 cm) is:

**Option C. 100 cm, 40 cm, 96 cm, and 68 cm.**